Tarski's undefinability theorem

Target entity: Tarski's undefinability theorem
Context triple: [liar paradox, relatedTo, Tarski's undefinability theorem]

• A. Hilbert’s program
  Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
• B. Remarks on the Foundations of Mathematics
  Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
• C. The Logical Syntax of Language
  The Logical Syntax of Language is Rudolf Carnap’s seminal 1934 work that systematically develops a formal, logical framework for analyzing the structure and rules of scientific languages, helping to found logical empiricism and modern philosophy of language.
• D. von Neumann paradox in set theory
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• E. Russell’s paradox
  Russell’s paradox is a foundational logical contradiction in naive set theory that reveals problems with sets that contain themselves, leading to major developments in modern logic and the axiomatization of set theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Tarski's undefinability theorem
Target entity description: Tarski's undefinability theorem is a fundamental result in mathematical logic showing that, in sufficiently strong formal systems, the notion of truth for the language of the system cannot be defined within that same language.

• A. Hilbert’s program
  Hilbert’s program was an influential early-20th-century initiative in the foundations of mathematics that sought to formalize all of mathematics and prove its consistency using finitistic methods.
• B. Remarks on the Foundations of Mathematics
  Remarks on the Foundations of Mathematics is a posthumously published collection of Ludwig Wittgenstein’s later writings that critically examines the nature of mathematical truth, proof, and practice from a philosophical and language-centered perspective.
• C. The Logical Syntax of Language
  The Logical Syntax of Language is Rudolf Carnap’s seminal 1934 work that systematically develops a formal, logical framework for analyzing the structure and rules of scientific languages, helping to found logical empiricism and modern philosophy of language.
• D. von Neumann paradox in set theory
  The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
• E. Russell’s paradox
  Russell’s paradox is a foundational logical contradiction in naive set theory that reveals problems with sets that contain themselves, leading to major developments in modern logic and the axiomatization of set theory.
• F. None of above. chosen